Question

A shopkeeper offers a 10% off-season discount to the customers and still makes a profit of 26%. What is the cost price for the shopkeeper on a pair of shoes marked at Rs 1120?

Answer 1

Hint – In this question let the cost price and the selling price of the pair of shoes be x and y rupees respectively. Use the concept that this 10% discount given will be on the marked price so formulate equations to get the value of x and y.

Complete step-by-step answer:
Let the cost price of the shoes be Rs. x
And the selling price of the shoes be Rs. y
It is given that the marked price of the shoes is Rs. 1120
Now it is given that the shopkeeper offers a 10% off-season discount to the customers.
So the discount is on the marked price.
So marked price minus 10% of marked price is equal to the selling price of the shoes.
Now construct the linear equation according to above information we have,
$ \Rightarrow 1120 - 1120 \times \dfrac{{10}}{{100}} = y$
Now simplify this equation we have,
$ \Rightarrow 1120 - 112 = y$
$ \Rightarrow y = 1008$ Rs.
Now it is also given that the shopkeeper still makes a profit of 26%.
Therefore the selling price is greater than the cost price of the shoes.
So the profit percentage is the ratio of difference of selling price and cost price to cost price multiplied by 100.
$ \Rightarrow 26 = \dfrac{{1008 - x}}{x} \times 100$
$ \Rightarrow 26x = 100800 - 100x$
$ \Rightarrow 126x = 100800$
$ \Rightarrow x = \dfrac{{100800}}{{126}} = 800$ Rs.
So the cost price of the shoes is Rs. 800
So this is the required answer.

Note – A profit is gained if and only if the selling price is greater than the cost price and thus why in calculating profit percentage we have subtracted the selling price with the cost price that is to be computed. In case of loss the cost price would have been greater than the selling price and thus in that case we would have taken out a loss percentage.